where \(\Delta ^1(\cdot ),\Delta ^2(\cdot ),\tilde{\Delta }^1(\cdot ),\tilde{\Delta }^2(\cdot )\)  are four \(\mathcal {F}_t\) -adapted processes, and \(z^{1,1^{\prime }},z^{2,1^{\prime }},\tilde{z}^{1,1^{\prime }},\tilde{z}^{2,1^{\prime }}\)  have good estimates similarly as \(x^1\) . However, different from the results in [1]} or [2]}, we find \(\tilde{\Delta }^1(\cdot )=\tilde{\Delta }^2(\cdot )=0\) . The main reason is that we subtract the jump part in the random interval \(\mathcal {O}\) . There is no need for such a term \(\tilde{\Delta }^1(t)\mathbb {1}_{\mathcal {O}},\tilde{\Delta }^2(t)\mathbb {1}_{\mathcal {O}}\)  in the third and fourth equality in (REF ), which is in accordance with the variational equation of \(x\)  in Section 3.1. Therefore, we mainly do Taylor expansions at \(\bar{x}_t,\bar{y}_t,\bar{z}^1_t+p_t\delta \sigma _1(t)\mathbb {I}_{E_{\epsilon }}(t),\bar{z}^2_t+p_t\delta \sigma _2(t)\mathbb {I}_{E_{\epsilon }}(t))\)  and \(\bar{\tilde{z}}_t^1,\bar{\tilde{z}}_t^2\)  for \(b_1,\sigma _1,\sigma _2, f_1, f_2, l\) , respectively.
